What kind of sequence is this? 6, 18, 54, 162, ... Choices: (A)arithmetic (B)geometric (C)both (D)neither

Check Arithmetic Sequence: Let's first check if the sequence is arithmetic by finding the differences between consecutive terms. Given sequence: 6, 18, 54, 162, ... Are the consecutive differences in the sequence equal? 18 - 6 = 12, 54 - 18 = 36, 162 - 54 = 108. The consecutive differences in the sequence are not equal.Check Geometric Sequence: Now, let's check if the sequence is geometric by finding the ratios between consecutive terms. Given sequence: 6, 18, 54, 162, ... Are the ratios between consecutive terms in the sequence equal? 18 / 6 = 3, 54 / 18 = 3, 162 / 54 = 3. Yes, the sequence has a common ratio of 3.Conclusion: Since the sequence does not have a common difference but does have a common ratio, we can conclude that the sequence is not arithmetic but is geometric.

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What kind of sequence is this? $\newline$ $6, 18, 54, 162, \dots$ $\newline$ Choices: $\newline$ (A) arithmetic $\newline$ (B) geometric $\newline$ (C) both $\newline$ (D) neither

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Algebra 2

Classify formulas and sequences

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Q. What kind of sequence is this?

\newline

6, 18, 54, 162, \dots

\newline

Choices:

\newline

(A) arithmetic

\newline

(B) geometric

\newline

\newline

(D) neither

Check Arithmetic Sequence: Let's first check if the sequence is arithmetic by finding the differences between consecutive terms. Given sequence: $6, 18, 54, 162, \ldots$ $\newline$ Are the consecutive differences in the sequence equal? $\newline$ $18 - 6 = 12$ , $54 - 18 = 36$ , $162 - 54 = 108$ . $\newline$ The consecutive differences in the sequence are not equal.
Check Geometric Sequence: Now, let's check if the sequence is geometric by finding the ratios between consecutive terms. Given sequence: $6, 18, 54, 162, \ldots$ $\newline$ Are the ratios between consecutive terms in the sequence equal? $\newline$ $\frac{18}{6} = 3, \frac{54}{18} = 3, \frac{162}{54} = 3.$ $\newline$ Yes, the sequence has a common ratio of $3$ .
Conclusion: Since the sequence does not have a common difference but does have a common ratio, we can conclude that the sequence is not arithmetic but is geometric.